Mathematics for the Million - Lancelot Hogben ***

This is one of the strangest maths books you are ever likely to encounter. Written in the 1930s and reissued in 2017, it's an attempt to provide mathematical instruction up to around A-level standard (though obviously the curriculum has changed a lot) for someone who, perhaps, doesn't respond well to the classroom and works better from self-teaching.

It's telling of the way popular science was considered in the period that apparently the author delayed publication as he was up for election to Fellowship of the Royal Society, which back then was dead against science popularisation.

Hogben, in a distinctive, mellifluous (if sometimes prolix) style, starts with the basics of arithmetic and leads us all the way through to calculus. Unlike his contemporaries, who were all for working through hundreds of geometry proofs for completeness, Hogben fills in the parts at each stage of mathematical development needed to reach the next stage and gives us no more.

The narrative here is very much centred on the application of mathematics through history. We see how geometry might have been used by Egyptian architects, and how trigonometry benefits those who need to navigate by the stars. The only problem with this learning-through-history approach is it can sometimes be hard to then relate what has been learned to uses in the present day.

Lancelot Hogben never intended this to be a fun read to pootle through just for the sake of it. The book is peppered with many exercises. It seems to be devised as a self-teach textbook of the future (as seen from the 1930s), throwing away the strictures of the rigid teaching approach of that period for something that is more approachable.

It's hard to say how well it delivers from the modern viewpoint of someone who has gone through all this stuff at school in a fairly traditional way. Clearly a lot of people decided it was a good approach back then: the book might not have made the 'million' in the title but certainly sold many copies.

To the modern eye, there is a danger of the book falling between two stools. It's not approachable enough to read purely for fun, but Hogben's distinctive, quirky style, combined with what is sometimes a rather tedious approach to the maths, means that it's not the best way for a modern reader, with no mathematical training, to learn about the subject. It stands best as a unique and fascinating oddity in the history of mathematical books for the general public - and as such is worth taking a look at.

Paperback:

Using these links earns us commission at no cost to you

Review by Brian Clegg

Comments

Beyond Belief - Helen Pearson *****

Apparently it comes as a surprise to many that medicine was not particularly scientific until the end of the twentieth century (to be honest, it's no surprise to me - we had a GP who used homeopathy in the 90s). Instead it was based on anecdotal guidance - the kind of thing that appeared to work. Evidence-based medicine has since improved the field, trying where possible to base decisions on evidence, ideally based on randomised controlled trials. The first part of Helen Pearson's book covers this well - though I think it's by far the least interesting part of what we discover. Instead what's truly fascinating is the rest of it, looking at a wide range of other fields where evidence was rarely properly used and that are only now starting to dip a toe in the water. These include social policy, policing, conservation, business and education. The main part of the book gives us examples of how bad these areas have been in terms of basing decisions on what's always been ...

In Seach of Sea Dragons - Matthew Myerscough ****

It's common advice to would-be authors of narrative non-fiction to open with something dramatic - Matthew Myerscough certainly does this with the story of his being trapped under an avalanche on Snowdon (while his girlfriend, also carried away remains on top of the snow unhurt). It certainly is dramatic, but seemed entirely disconnected from the reason I got the book, which was to read about fossil collecting. Luckily, though, in the second chapter we get into a more conventional 'how I got interested in fossils as a boy'. Having recently reviewed Patrick Moore's autobiography and noting that astronomy was one of the few sciences where amateurs can still make a contribution, it came to mind that palaeontology is another - Myerscough is a civil engineer by trade, but just as amateur astronomers can find new details in the skies, so amateur fossil hunters have been searching for these relics for centuries. When I give talks in junior schools, the two topics that guarant...

The Infinity Machine - Sebastian Mallaby ****

It's very quickly clear that Sebastian Mallaby is a huge Demis Hassabis fan - writing about the only child prodigy and teen genius ever who was also a nice, rounded personality. After a few chapters, though, things settle down (I'm reminded of Douglas Adams' description of the Hitchhiker's Guide to the Galaxy ) and we get a good, solid trip through the journey that gave us DeepMind, their AlphaGo and AlphaFold programs, the sudden explosion of competition on the AI front and thoughts on artificial general intelligence. Although Mallaby does occasionally still go into fan mode - reading this you would think that AlphaFold had successfully perfectly predicted the structure of every protein, where it is usually not sufficiently accurate for its results to have direct practical application - we get a real feel for the way this relatively unusual company was swiftly and successfully developed away from Silicon Valley. It's readable and gives an important understanding of...

Search This Blog